It can certainly cut both ways.
I'd give the nod to us in the rain for a couple reasons. Our offensive line should dominate. I expect a big dose of Folston, Cam, Bryant early. They won't be able to handle our line without help from their secondary. As soon as they start flying to the line in run support, Kelly will hit them over the top with play action. We're going to catch them cheating up and it's hard for a DB to recover on a slick surface. I doubt our secondary will be relied upon as heavily to stop the run. They'll have a chance to sit back, read their keys and play honest football.
We've practiced on our own field. Not much and probably not in the rain, but we will be more familiar with the surface and it'll give us an advantage, even if it is slight.